Structure, energetics and thermodynamics of copper–vacancy clusters in bcc-Fe: An atomistic study

A combination of on-lattice simulated annealing based on Metropolis Monte Carlo simulations and off-lattice relaxation by Molecular Dynamics is applied in order to determine the structure and energetics of coherent copper–vacancy clusters in bcc-Fe. The most recent interatomic potential for Fe–Cu alloys is used. About 150 clusters consisting of up to 200 monomers (vacancies or copper atoms) are investigated. The atomic structure and the formation energy of the most stable configurations as well as their total and monomer binding energy are calculated. All clusters show facets which correspond to the main crystallographic planes. In the case of mixed clusters a core–shell structure is found where Cu atoms coat the outer surface of vacancy clusters. These findings are in agreement with previous theoretical results and with indications from measurements. For small clusters the total binding energy determined in this work shows a good agreement with literature data obtained by first-principle calculations. For further application in rate theory and object kinetic Monte Carlo simulations compact and physically-based fit formulae are derived from the atomistic data for the total and the monomer binding energy. The fit is based on the classical capillary model and the core–shell structure of the mixed clusters is explicitly taken into account. An atomistic nucleation model is established, and for typical irradiation conditions the nucleation free energy of pure vacancy and pure copper clusters as well as the critical size for cluster formation are estimated.